There have been significant improvements over the years in the willingness and expertise with which overseas schools are able to support children with mild to moderate special needs. Many of them have added a specialist in learning disabilities to their faculty, sometimes offering an hour or two in a special classroom, more often supporting teachers in the regular classroom. Virtually all schools offer special support to English language learners. Much less frequently, you may find a psychologist, speech specialist, or even occupational therapist on the school staff; more often, there will be links to such professionals in the community, if they exist. You will not find the array of specialists you can expect to assist you child in the public schools at home.
Remember that these are independent schools much like mainstream private schools in the United States. They do not necessarily see themselves as serving all children, although they do generally attempt to give special consideration to dependents of U.S. Government employees. The older, larger schools, especially those in well-to-do capitals, tend to be highly selective and academically demanding. While most directors and teachers are sympathetic to incoming students, expectations are relatively high and the support offered to students with special needs, even by specialists, should be seen in that context. Smaller, growing schools may be more flexible but are generally also operating with limited resources, very much like smaller schools in the United States that are trying to get on their feet.
Additionally, while the faculty is likely to include some U.S.-trained teachers, you can expect a truly international group who will bring a richness of outlooks to the educational scene. They may not, however, see your child with special needs in the same way that U.S.-trained teachers do, may use different terminology and follow different theories, and may not be trained to provide the accommodations that you have found so important in making your child successful. Don't give up, but be prepared for tactful negotiations, and bring as much knowledge as you can to help teachers see that your child can be successful with feasible classroom accommodations.
If your child has attention deficit disorder, and/or quirks of personality that affect classroom behavior, then come with an explicit list of recommended accommodations from a psychologist and previous teachers. (A letter from a previous teacher who had a special feel for your child can be a real help.) Probably not all of these accommodations are going to be put into operation, and almost certainly not all the time. Be patient, and do as much as you can to enable your child to advocate for himself/herself when something would be helpful. Stay in touch with the teacher(s) and continually give positive feedback about things that are happening at school that have value for your child.